A pedestal in a craft store is in the shape of a triangular prism. The bases are right triangles with side lengths of 12 centimeters, 16 centimeters, and 20 centimeters. The store owner wraps a piece of rectangular cloth around the pedestal, but does not cover the identical bases of the pedestal with cloth. The area of the cloth is 192 square centimeters.

A)What is the distance around the base of the pedestal? How do you know?
B)What is the height of the pedetal? How did you find your answer?
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A) To find the distance around the base of the pedestal, we need to calculate the perimeter of the triangular base.

The sides of the triangular base are given as 12 cm, 16 cm, and 20 cm. To find the perimeter, we add together the lengths of all three sides.

Perimeter = 12 cm + 16 cm + 20 cm = 48 cm

So the distance around the base of the pedestal is 48 centimeters.

B) To find the height of the pedestal, we can use the area of the cloth that was wrapped around it. The area of the cloth is given as 192 square centimeters.

The area of a rectangle can be calculated using the formula: Area = Length x Width.

Let's assume the length of the cloth is L cm and the width is W cm.

From the given information, we know that the cloth does not cover the identical bases of the pedestal. This means that the length of the cloth is equal to the perimeter of the base (48 cm) minus the sum of the two identical sides (12 cm + 12 cm).

L = Perimeter - (Side1 + Side2)
L = 48 cm - (12 cm + 12 cm)
L = 48 cm - 24 cm
L = 24 cm

So the length of the cloth is 24 centimeters.

We can now use the formula for the area of the cloth to find the width of the cloth.

Area = Length x Width
192 cm² = 24 cm x Width

Solving for Width:
Width = 192 cm² / 24 cm
Width = 8 cm

Now, we have the width (8 cm) and length (24 cm) of the cloth. The height of the pedestal is equal to the width of the cloth, which is 8 centimeters.

To summarize:
A) The distance around the base of the pedestal is 48 centimeters.
B) The height of the pedestal is 8 centimeters.